Delineation of Groundwater Potential Zones using Remote Sensing and GIS Techniques in Kanakanala Reservoir Subwatershed, Karnataka

Abstract

For almost 30 years, paleontologists have analyzed evolutionary sequencesin terms of simple null models, most commonly random walks. Despitethis long history, there has been little discussion of how modelparameters may be estimated from real paleontological data. In thispaper, I outline a likelihood-based framework for fitting and comparingmodels of phyletic evolution. Because of its usefulness and historicalimportance, I focus on a general form of the random walk model. Thelong-term dynamics of this model depend on just two parameters: themean ({micro}step) and variance ({sigma}2step) of the distributionof evolutionary transitions (or "steps"). The value of {micro}stepdetermines the directionality of a sequence, and {sigma}2step governsits volatility. Simulations show that these two parameters can beinferred reliably from paleontological data regardless of how completelythe evolving lineage is sampled. In addition to random walk models,suitable modification of the likelihood function permits considerationof a wide range of alternative evolutionary models. Candidate evolutionarymodels may be compared on equal footing using information statisticssuch as the Akaike Information Criterion (AIC). Two extensions tothis method are developed: modeling stasis as an evolutionary mode,and assessing the homogeneity of dynamics across multiple evolutionarysequences. Within this framework, I reanalyze two well-known publisheddata sets: tooth measurements from the Eocene mammal Cantius, andshell shape in the planktonic foraminifera Contusotruncana. Theseanalyses support previous interpretations about evolutionary modein size and shape variables in Cantius, and confirm the significantlydirectional nature of shell shape evolution in Contusotruncana. Inaddition, this model-fitting approach leads to a further insightabout the geographic structure of evolutionary change in this foraminiferanlineage.